1. Field of the Invention
This invention relates generally to hard disk drive systems and, more particularly to the control system determining the position of the read/write head over the storage disk. The read/write head is mounted on an arm, the arm in turn is driven by a servo-actuator unit relative to the tracks on the disc. The control system is designed to minimize the time to move the read/write head from an initial position over the tracks of the storage disk to a final position over the tracks of the storage medium, a mode of operation referred to as a "seek" operation.
2. Description of the Related Art
The reduction of the seek time is becoming more difficult as the tracks on the storage disk become more dense. The arm, upon which the read/write head is mounted, and the servo actuator motor (or dc motor) driving the arm are referred to as the hard disk drive "plant". The plant is characterized by electrical and mechanical systems which can be non-linear, which can be unknown, and which can be a function of environmental (and/or time-dependent) parameters. Prior art plant control units which perform the seek function are unable to achieve the minimum seek time within the parameters and constraints of the end point accuracy and settling requirements.
Referring to FIG. 1, a block diagram of a hard disk drive closed-loop plant control unit for a hard disk drive plant, according to the prior art, is shown. Signals representing the desired and the actual position of the read/write head are applied to input terminals of difference amplifier 10. Position loop component 11 receives the output signal from difference amplifier and applies the filtered signal to a first terminal of difference amplifier 12. A second terminal of difference amplifier 12 has a signal representing the read/write head velocity applied thereto. (The head velocity is frequently referred to herein as the head delta position.) The output signal of difference amplifier 12 is applied to an input terminal of velocity loop component 13. The output signal of velocity loop component 13 is applied to a first terminal of difference amplifier 14. A second input terminal of difference amplifier 14 receives a signal representative of the actuator current. The output signal of difference amplifier 14 is applied to current loop component 15. The output signal of current loop component 15 is applied to a power supply saturation analog unit 16. The output signal from analog unit 16 is applied to one input terminal of difference amplifier 17. A second input terminal of difference amplifier 17 receives a signal indicative of induced emf from an output terminal of back-emf component 102. The output signal from difference amplifier 17 is applied to the actuator impedance analog unit 18. The output signal from the analog unit 18 is applied to the second input terminal of difference amplifier 14 and to the torque/inertia analog unit 19. The output signal from analog unit 19 is applied to the second input terminal of difference amplifier 12, to an input terminal of back-emf component 102, and to 1/s component 101.
The output signal of 1/s component 101 is applied to the second terminal of difference amplifier 10 and determines the position of the read/write head. The position is also referred to herein as the actual position or relative position, i.e., measured with respect to the final track position.
Difference amplifier 17, actuator impedance analog unit 18, torque/inertial analog unit 19, 1/s component 101 and back-emf component 102 represent a model of the hard disc drive plant. Actuator impedance unit 18 provides the analog of the actuator unit impedance (resistance and inductance). Torque/inertial analog unit 19 provides the analog of the actuator torque constant (K.sub.t), the rotational inertial (J) and the integration (1/s), providing the velocity from the acceleration. 1/s component 101 provides the analog of integration from velocity to position. And back-emf component 102 provides the analog of the back emf constant K.sub.b of the voltage generated by the actuator motor.
Conventional closed-loop controllers typically perform the seek-to-track function by using estimates of the position, velocity and acceleration (plant states) information as feedback information to close the loop. The closed-loop controllers can be implemented using either analog or digital technology. The closed-loop controllers employing the analog technology, attempting to provide a minimum seek time can be complicated by uncontrollable variables such as loop gain variation, power supply variations, and large plant variations. Closed-loop controllers in digital technology provide improved performance through the use of more complex mathematical algorithms to compensate for offset and to compensate for some loop parameter variations. Closed-loop analog controllers of the prior art provide an average seek time of approximately 15 milliseconds (msec). Using digital technology, this seek time can be reduced to a range of between 10 and 12 msec. It is anticipated that future requirements, derived from the need for higher positional accuracy resulting from the higher track density on the storage disks, will require seek times of approximately 6 msec.
Referring to FIG. 2, a model of the hard disk drive unit plant expressed in terms of Laplace transform variables is shown. A difference amplifier 20 has voltage drive signal applied to a first input terminal and a signal from the back-emf component 201 applied to a second input terminal. The output of difference amplifier 20 is amplified to first input terminal of difference amplifier 21 while an output signal from actuator resistance component 202 is applied to the second input terminal of difference amplifier 21. The output signal from difference amplifier 21 is applied to the actuator impedance component 22. The output signal from the output impedance component 22 is applied to 1/s analog component 23. The output signal from the 1/s analog component 23 is applied to the actuator resistance filter 202 and to the actuator torque/inertia component 24. The output signal from the actuator torque/inertia component 24 is applied to a first input terminal of difference amplifier 25, while an output signal from coulomb friction analog unit 29 is applied to a second input terminal of difference amplifier 25. The output signal of difference amplifier 25 is applied to resonance analog unit 26. The output signal from the resonance analog unit 26 is applied to 1/s analog component 27. The output signal for 1/s analog component 27 is applied to an input terminal of back-emf component 201, to and input terminal of coulomb friction analog component 29, and to an input terminal of 1/s analog component 28. The output signal from 1/s analog component 28 is indicative of the position of the read/write head. The major components of the plant model of FIG. 2 represent the rotary actuator (dc torque) characteristics, the head and actuator inertia, the mechanical resonance of the plant, and the mechanism friction. The model includes a non-linear representation, i.e., the saturation of the power supply at its limits (.+-.12 volts), mechanism resonance, and friction on the seek time performance. Typical values for the parameters of the actuator plant unit are: the actuator resistance R=8.0 ohms, the actuator inductance L =1.0 mH, the actuator torque constant K.sub.t =13 oz-in/amp, the back-emf constant K.sub.b =0.092 v-sec/rad, and the actuator inertia J=0.0009 oz-in-sec.sup.2.
Referring once again to FIG. 2, the transfer function for input voltage to output velocity (neglecting mechanism resonance and friction can be described by the Laplace equation: EQU .omega.(s)/V(s)=(1/K.sub.b)/{1+JRs/K.sub.b K.sub.t }{1+Ls/R} (1)
Assuming that JR/K.sub.b K.sub.t &gt;&gt;L/R, an assumption normally interpreted that the mechanical time constant is much greater than the electrical time constant and generally true for hard disk drive actuators, this equation can be reduced to a second order differential equation; EQU d.sup.2.theta./dt.sup.2 +d.theta./dt(1/.tau..sub.m)=.+-.V/(K.sub.b.tau..sub.m) (2)
where .+-.V is the variable power supply voltage and .tau..sub.m =JR/(K.sub.b K.sub.t), the mechanical time constant. The term .+-.V/(K.sub.b.tau..sub.m) is the (sign dependent) acceleration or deceleration capability of the plant and can be defined as .+-.A. To accelerate the actuator head, +A would be applied and the time dependence of the state equation becomes: EQU position .theta.=.tau..sub.m At-.tau..sub.m.sup.2 A(1-e.sup.t/.tau.m) EQU velocity (delta) d.theta./dt=.tau..sub.m A(1-e.sup.t/.tau.m) EQU acceleration d.sup.2.theta./dt.sup.2 =Ae.sup.t/.tau.m)
Similarly, when the actuator is decelerating, i.e., -A is applied to the plant, then the solution for the differential equation would be EQU position .theta.={.tau..sub.m (d.theta./dt).sub.sw +.tau..sub.m.sup.2 A}(1-e.sup.t/.tau.m)-.tau..sub.m At+.theta..sub.sw EQU velocity (delta) d.theta./dt=(d.theta./dt).sub.sw e.sup.t/.tau.m -.tau..sub.m A(1-e.sup.t/.tau.m) EQU deceleration d.sup.2.theta./dt.sup.2 =-{A+(d.theta./dt).sub.sw /.tau..sub.m }e.sup.t/.tau.m
where .theta..sub.sw and (d.theta./dt).sub.sw are states (initial conditions) at the time of the application of the -A force.
A simple definition of a controller objective is movement of the actuator read/write head from an initial state (.theta.=.theta..sub.i, d.theta./dt=0, and d.sup.2.theta./dt.sup.2 =0) to a final state (.theta.=.theta..sub.f, d.theta./dt=0, and d.sup.2.theta./dt.sup.2 =0) in the minimum time. The optimum control procedure to accomplish this minimum seek time movement requires N-1 drive signal polarity reversals for a system described by an N.sup.th order state equation. Therefore, with the second order system described by the above equations, the minimum seek time will be accomplished with one polarity reversal from +V to -V at some point during the transition from the initial to the final state. The steps to accomplish this minimum time movement can be summarized as follows:
1) Apply full power supply voltage to the actuator to accelerate from some initial state .theta..sub.i to a switch point .theta..sub.sw. PA1 2) Apply full reverse power supply voltage to the actuator to decelerate from the switch point .theta..sub.sw to the desired final state .theta..sub.f. PA1 3) At .theta.=.theta..sub.f, initiate track control, with d.theta./dt=0 and d.sup.2.theta./dt.sup.2 =0 if .theta..sub.sw is chosen correctly.
FIG. 3 illustrates a computer simulation of an example of a seek operation for a movement of 0.122 radians. In this simulation, a maximum voltage of +12 volts is applied to the plant. As a result, the velocity of the actuator head accelerates to 50 radians/sec and the position error decreases to slightly greater than 50 milliradians (mrad) at a time of approximately 3 msec. At this time, the decision is made to reverse the voltage to the maximum negative value of -12 volts. The actuator decelerates to zero position error and zero velocity in less than 6 msec.
The minimum seek time illustrated by FIG. 3 relies on the fact that the optimum switch point, .theta..sub.sw, is properly determined. If a controller can be designed which achieves the foregoing sequence for applying the maximum available voltage with the correct timing sequence for any arbitrarily-sized seek operation, then the controller achieves the minimum seek time for the hard disk drive unit. Furthermore, when the controller can accomplish this desired sequence in the presence of expected plant non-linearity and in the presence of parameters which can vary with time and with temperature, then the controller has wide-spread applicability and utility.
A need has been therefore been felt for apparatus and an associated technique which will approximate a minimum time for a seek operation in a hard disk controller in the presence of non-linearity of the actuator unit and in the presence of time-varying and temperature dependent parameters.